How do you simplify ${2 - 4 [3 + {(5 + \frac{1}{2})}^{2}]} - 7$ ${2-4[3+(5+1/2)^2]}-7$ ?

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How do you simplify ${2 - 4 [3 + {(5 + \frac{1}{2})}^{2}]} - 7$ ${2-4[3+(5+1/2)^2]}-7$ ?

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Answer 1 · 2016-09-18T08:00:11

$- 138$ $-138$

Explanation:

In mixed operation calculations, always count the number of terms first. Each term must simplify to a single number.

Within each term, the order of operations is brackets first , then from strongest to weakest operations,
Powers and roots
Multiply and divide

Add and subtract is done last from left to right

${2 - 4 [3 + {(5 + \frac{1}{2})}^{2}]} - 7 \leftarrow$ ${2-4[3+(color(red)(5+1/2))^2]}-7" "larr$ there are 2 terms

Start with the innermost bracket.

= ${2 - 4 [3 + {(\frac{11}{2})}^{2}]} - 7 (\to 5 + \frac{1}{2} = 5 \frac{1}{2} = \frac{11}{2})$ ${2-4[3+color(red)((11/2)^2)]}-7" "(rarr 5+1/2 = 5 1/2 =11/2)$

= ${2 - 4 [3 + \frac{121}{4}]} - 7 \leftarrow$ ${2color(red)(-4[3+121/4]}}-7" "larr$ distributive law with -4

= ${2 - 12 - 121} - 7$ ${2-color(red)(12-121}}-7$

= $- 131 - 7$ $-131-7$

= $- 138$ $-138$

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How do you simplify ${2 - 4 [3 + {(5 + \frac{1}{2})}^{2}]} - 7$ ${2-4[3+(5+1/2)^2]}-7$ ?

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How do you simplify ${2 - 4 [3 + {(5 + \frac{1}{2})}^{2}]} - 7$ ${2-4[3+(5+1/2)^2]}-7$ ?